a lot for sale is shaped like a trapezoid.

Question

a lot for sale is shaped like a trapezoid. The bases of the trapezoid represent the widths of the front and back yards. The width of the back yard is twice the width of the front yard. the distance from the front yard to the backyard, or the height of the trapezoid, is equal to the width of the back yard. Find the width of the front and back yards, given that the area is 6000 square feet. Round to the nearest foot

Answer 1

the formula for the Area of a trapezoid is A = h (b1 +b2)/2

 

we are given that A = 6000f²

we are told that h = width of back yard

let b1 = width of front yard, then  back yard = 2b1, and h = 2b1

 

so, 6000f² = 2b1 ((b1 + 2b1)/2

which becomes 6000f² = 3b1²

2000f2 = b1²

b1 ≅ 44.72f

 

Proof: 6000f² = 2•44.72((44.72 + 89.44)/2) = 89.44•67.08 = 6000f²